On each PvP round, meaning not a loot round, every player faces a random opponent on their own board. In any given round, your units are fighting on two boards: defending your HP on your board, and attacking a random player on their own board.
The outcomes of these fights are not tied to each other in any way, other than using the same pieces. When a message shows that a player repelled your attack, it means that that player won on their own board, regardless of what happened on your board.
Repelling an attack causes no HP damage to the attacker, and the game only ends when all but one players have ran out of HP, it does not use a single-elimination format. When only two players are left, if they both manage to repel the enemy's attack, neither of them will lose HP and the game can keep stretching until one of them eventually loses.